I think that part of the reason why Roosevelt was so successful in navigating in the perils of World War II was because he understood the need to represent different elements in different situations. To the American people, there was a clear appeal to the need to make the world "safe for democracy." The idea of America being "an arsenal for democracy" and the use of the Fireside Chats were instrumental to this end. Roosevelt was able to barter his own credibility with the American people to convince them the need for war was a pressing one. The attack on Pearl Harbor helped to make his case for him. To the industrialists in America, Roosevelt presented the war as an opportunity for huge production and growth, speaking the language of the industrialist in a specific situation. To the foreign community, Roosevelt was a skilled pragmatist who understood the need to forge alliances in pursuit of a common good. The fact that Roosevelt understood how to be a successful leader to different factions needed for success represents how he was able to navigate the trying situation that World War II posed.
I would argue that there were two major reasons why Franklin Roosevelt was very succesful in dealing with the challenges of WWII.
First, FDR was a very confident man who did not worry much about what others thought about his decisions. He was decisive in his decision-making. This is a very important trait in a leader, especially during war time.
Second, FDR was a very good politician. This was especially important in WWII because of the fact that the US was part of a coalition of allies. FDR had to balance the demands of the various countries involved in the alliance while also dealing with demands from US politicians and US military leaders. His ability to juggle these various demands was important in the Allies' ability to fight the war effectively.